SOLUTION: Find the smallest positive integer $N$ such that N &\equiv 2 \pmod{5}, \\ N &\equiv 2 \pmod{7}.

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Find the smallest positive integer $N$ such that N &\equiv 2 \pmod{5}, \\ N &\equiv 2 \pmod{7}.      Log On


   

Question 1207721: Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{5}, \\
N &\equiv 2 \pmod{7}.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the smallest positive integer N such that
N = {2 mod 5},
N = {2 mod 7}.
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See the solution by @greenestamps.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


N is the smallest positive integer that is both 2 more than a multiple of 5 and 2 more than a multiple of 7.

The answer, trivially, is N=2.

ANSWER: 2